hw3 (1)

1. Consumption and saving definitions Suppose Karen gets a sales bonus at her place of work that gives her an extra $600 of disposable income. She chooses to spend $480 and save the remaining $120.   Mathematically, it must always be true that: Consumption  =  =

Tim is buying pizza and salad for a company lunch. Suppose that a slice of pizza costs $4.00, and a bowl of salad costs $5.00. Let ♬ be the amount in dollars that Tim spends on pizza and salad. If Tim buys P slices of pizza and S bowls of salad, then the total amount of money he spends (B) can be represented by the equation Now rearrange the equation you wrote above so that S is written in terms of E and P. The quantity of salad he buys can be represented by the equation Suppose Tim has $40.00 to spend on pizza and salad; that is, E = $40.00. Complete the following table with the values of P or S that make the equation true. Hint: To complete the first row, determine the number of salad bowls Tim can purchase with $40.00, when the number of pizza slices he purchases is 0. Budget Pizza (Dollars) (Slices) 40.00 0 40.00 5 40.00 Use the black line (plus symbols) to plot the line illustrating the combinations of pizza and salad that Tim can purchase with a budget of $40.00. SALAD (Bowis) 14…

Kenji is buying salad and pizza for a company lunch. Suppose that a bowl of salad costs $3.00, and a slice of pizza costs $4.00. Let E be the amount in dollars that Kenji spends on salad and pizza. If Kenji buys S bowls of salad and P slices of pizza, then the total amount of money he spends (E) can be represented by the equation Now rearrange the equation you wrote above so that P is written in terms of E and S. The quantity of pizza he buys can be represented by the equation Suppose Kenji has $48.00 to spend on salad and pizza; that is, E= $48.00. Complete the following table with the values of S or P that make the equation true. Hint: To complete the first row, determine the number of pizza slices Kenji can purchase with $48.00, when the number of salad bowls he purchases is 0. Pizza Budget Salad (Dollars) (Bowls) (Slices) 48.00 0 48.00 48.00 8 0

Rajiv is buying pizza and salad for a company lunch. Suppose that a slice of pizza costs $2.00, and a bowl of salad costs $4.00. Let E be the amount in dollars that Rajiv spends on pizza and salad. If Rajiv buys P slices of pizza and S bowls of salad, then the total amount of money he spends (E) can be represented by the equation Now rearrange the equation you wrote above so that S is written in terms of E and P. The quantity of salad he buys can be represented by the equation Suppose Rajiv has $32.00 to spend on pizza and salad; that is, E = $32.00. Complete the following table with the values of P or S that make the equation true. Hint: To complete the first row, determine the number of salad bowls Rajiv can purchase with $32.00, when the number of pizza slices he purchases is 0. Budget Pizza Salad (Dollars) (Slices) (Bowls) 32.00 32.00 8 32.00 Use the black line (plus symbols) to plot the line illustrating the combinations of pizza and salad that Rajiv can purchase with a budget of…

Kenji is buying pizza and salad for a company lunch. Suppose that a slice of pizza costs $2.00, and a bowl of salad costs $4.00. Let E be the amount in dollars that Kenji spends on pizza and salad. If Kenji buys P slices of pizza and S bowls of salad, then the total amount of money he spends (E) can be represented by the equation Now rearrange the equation you wrote above so that S is written in terms of E and P. The quantity of salad he buys can be represented by the equation Suppose Kenji has $32.00 to spend on pizza and salad; that is, E= $32.00. Complete the following table with the values of P or S that make the equation true. Hint: To complete the first row, determine the number of salad bowls Kenji can purchase with $32.00, when the number of pizza slices he purchases is 0. Budget Pizza Salad (Dollars) (Slices) (Bowls) 32.00 0 32.00 8 32.00 00 0

Use the following diagrams to answer this question 0 0 LRAS, Y, Y₂ Panel (a) LRAS, Y, Y₂ Panel (c) SRA S, AD₂ AD₁ Y SRA S, AD₁ SRA S₂ P₁ P₂ 0 P₂ 0 LRAS, SRAS, K AD₂ Y₂ Y₁ Panel (b) LRAS, SRA S, Y₂ Y₁ Panel (d) SRAS, AD, Y In panel (d), Which one of the following statements is (are) correct? O A. At E1, the economy is in short-run macroeconomic equilibrium, and GDP gap # 0. O B. At E2, the economy is in long-run macroeconomic equilibrium, and GDP gap > 0. O C. At E2, the economy is in short-run macroeconomic equilibrium, and GDP gap < 0. OD. Both A) and B) are correct.

C. Suppose your neighbor is a physics major who also races motorcycles, and she tells you that horsepower can be expressed in terms of the following equation: H = MDA/S where M=mass, D-distance, A=acceleration and S and H are as defined above. Based on this conversation with your neighbor, you decide to change the functional form of the relationship to include 1/H rather than H as an explanatory variable because that's the appropriate theoretical relationship between the two variables. Estimate the above equation, substituting 1/H for H. Which of the two models do you prefer and why?

Consumption/Savings 1000 800 600 400 200 0 -200 Select one: 200 400 600 800 1000 1200 1400 1600 S Refer to the graph above to answer this question. What is the equation for the saving function? A. S=200+ 0.4Y. B. S=-200+ 0.6Y. X C. S-200+ 0.8Y. OD. S-200 +0.2Y. OE. S=200 - 0.2Y. Income

3. Today is a great day for Stephanie. She played the MegaBillions lottery and won $25. In addition, while hanging out at Ho-Chung Bingo & Casino, she saw another patron drop a $16 voucher. Stephanie did not say anything and kept the voucher for herself. Later, Stephanie realized that she had lost her wallet which had both the MegaBillions ticket & $7 inside. Assume Stephanie's value function is defined as follows: SVE, v(x) = if x >0 if r < 0 What is the difference in the value of these outcomes if Stephanie in- tegrates them as compare to the value she would get from segregating them?

For a certain company, the cost for producing x items is 60x + 300 and the revenue for selling x items is 100x – 0.5x². - The profit that the company makes is how much it takes in (revenue) minus how much it spends (cost). In economic models, one typically assumes that a company wants to maximize its profit, or at least wants to make a profit! Part a: Set up an expression for the profit from producing and selling x items. We assume that the company sells all of the items that it produces. (Hint: it is a quadratio polynomial.) Part b: Find two values of x that will create a profit of $300. The field below accepts a list of numbers or formulas separated by semicolons (e.g. 2; 4; 6 or x + 1; x – 1). The order of the list does not matter. To enter va, type sqrt(a). x = Part c: Is it possible for the company to make a profit of $15,000?

“How to allocate limited resources to their best use is the very first and fundamental principle that you guys learn in a first course in both economics and finance.” Explain how the concepts and techniques covered in the various topics in this course can help address the issue. [Hint: Think about how NPV, as an investment decision rule, addresses the efficient allocation of limited resources problem. Specifically, why an investment project being “profit-making” may still be value- destroying and result in misallocation of resources?]

4. Suppose that Kyle's value function for cookies can be described as follows: x ≥0 x < 0 a) What does λ denote? V(x) x b) Assuming 2 = 2 fill in the following table: -5 -4 -3 -2 -1 0 1 2 3 4 = 5 s x, Ιλπ, V(x) c) Plot Kyle's value function in a diagram and comment on its shape.

The relationships between some economic variables w, y, and z and another economic variable, x, are shown in the graph above. Notice that the horizontal axis is labeled “x” since they are all functions of x but the vertical axis is not labeled. 1-1 Does the vertical axis need a label in order for you to be able to understand the graph?1-2What value of x minimizes w?

With the use of an example, briefly explain the main difference between the ex-ante and the ex-post opportunity cost of capital. Why does this matter for the evaluation of an investment decision? In what ways can managers utilise the distinction between ex-ante and ex-post opportunity cost of capital when deciding on the firm’s strategy?

Rue operates a food truck on Florida beaches, where she sells paninis and drinks, which she can sell for $8.00 and $4.00, respectively. Rue uses all of the money she makes to purchase theme park tickets, which cost $96.00, and her only other income comes from dividend payments of $32.00 from her investment portfolio. Let ?1 represent paninis, ?2 represent drinks, ? represent tickets, and ? represent dividend income. Complete Rue's budget equation: 8 ?1 + 4 ?2 + 32 = 96 ? Two of Rue's friends are coming to town,

Explain carefully using a graph (that is drawn to scale) to describe a situation where it is an optimal strategy for members in a two-person household to engage in equal consumption of total household income.

3. Suppose that the utility functions u(x, y) and v(x, y) are related by v(x, y) = f(u(x, y)). In each case below, check if f is a positive monotonic transformation' of u. (a) f(u) = 3.141592u (b) f(u) = 5000 – 23u (c) f(u) = ! %3D (d) f(u) = -u-1

Suppose that Y=MX+b, where Y=consumption, b=consumption at zero income, M=slope, and X=income(i) Are Y and X positively related or are they negatively related?(ii) If graphed, would the curve for this equation slope upward or slope downward?(iii) Are the variables Y and X inversely related or directly related?(iv) What is the value of Y if b=10, M=.50, and X=200?(v) What is the value of X if Y=100, b=10, and M=.25?

Suppose a consumer has $1500 in the current time period and $1100 in the future time period.Suppose also that the consumer can borrow and lend freely and, unless otherwise specified, borrowing and lending interest rates are the same. (a) If the interest rate between time periods is 50%, what is the budget constraint between consumption in the present and consumption in the future? (B) If the interest rate at which the consumer can borrow is 75% but the rate at which she can lend is25%, what is the budget constraint? (C) Suppose the interest rate is 50%. If the consumer has to pay a fee of 10% of the loan amount in order to borrow money, what is the budget constraint?

The following table contains data on the relationship between saving and income. Rearrange these data into a meaningful order and graph them on the accompanying grid. What is the slope of the line? The vertical intercept? Interpret the meaning of both the slope and the intercept. Write the equation that represents this line. What would you predict saving to be at the $12,500 level of income?

How would you demonstrate part b) diagramatically 6. Assume you can work as many hours you wish at £12 per hour (net of tax). If you do not work, you have no income. You have no ability to borrow or lend, so your consumption, c, is simply equal to your income. a) Derive and plot the feasible set, between daily values of consumption c, and “leisure”, l.  Label the values at the intercepts (the points where the feasible frontier cuts the two axes). b) Assume that your optimal choice of consumption and leisure is to work 8 hours per day. Illustrate this choice diagrammatically using the feasible set and indifference curves.

3. Consider a parent who is altruistic towards her child, but also cares about her own consumption. The parent's utility over her own consumption and that of her child is up = log(co) +a log(ci) where c is the child's consumption, and a > 0 is the degree of parental altruism. Suppose that the parent can invest in the child's human capital by spending money (e) on her education; education generates human capital h /() and human capital is paid at rate w. The parent has a total income of (a) Write down an expression for the child's future consumption in terms of the parent's choice of e. (b) Now write down the Lagrangian for the parent's decision problem.

Suppose that private savings and investment functions are given by: S = −c0 + (1 − c1)(Y − T) I = b0 + b1Y with G = T = 0. Assume 0 < b1 < 1−c1 < 1 (i.e. that slope of the savings curve is steeper than that of the investment curve). (a) Model Basics: Draw a graph of the investment=savings model with S,I on the vertical axis, and Y on the horizontal axis. Clearly label the 1) specific values of each intercept, 2) specific values of the slopes of each curve. (b) Suppose consumers choose to save more by reducing consumption at any given level of income, so that c0 declines. Show this on the graph. What are the effects of this change on 1) output, 2) the level of private savings, 3) the level of investment. (c) Briefly describe the economic intuition behind your results. Why is this called the paradox of thrift? (1-2 sentences is fine). (d) Deriving the Model: Show that the equilibrium condition Y = C + I + G implies I = S + T − G

it is given that the ratio of APS to APC is 2/7 Calculate the ratio of Consumption to savings

Q2)Complete the following table and illustrate by graph following variables (TFC. TVC. TC. MC)   TFC TVC   MC ATFC ATVC ATC   20                 35               38               40               55

Your landlord lets you grow plants in the yard, but limits the amount of water you may give them to 24 gallons a month. You may plant cacti and/or palms. Each month, a palm tree requires 8 gallons of water; a cactus needs 2. Put QP, the number of palms grown, on the vertical axis, and use QC for how many cacti you grow. Assume that it is possible to grow fractional quantities of both types of plant, for example, % of a palm tree. Show Transcribed Text 4. What is the opportunity cost of maintaining a cactus (measured in palm trees forgone)? A. 1 C. D. B. E. F. G. H. SABCDEFGH 4 1/4 1/3 D. 24 3 1 B. 4 5. What is the opportunity cost of maintaining a palm tree (in cacti forgone)? A. Cannot be known from the information provided None of the above (Explain why: C. 1/4 1/3 S C E. 24 F. 3 G. Cannot be known from the information provided H. None of the above (Explain why: Outside it On it At one of its endpoints 6. Where is the combined output of 2 palms and 3 cacti in relation to the PPF? A.…

A) Complete the following table B) Illustrate the following variable by graph: (TFC, TVC, TC) Q TFC TVC TC MC ATFC ATVC ATC 20 20 30 3. 45 80 2.

Geometric gradient. C.1.) A graduating class of civil engineers decides they will present the engineering college with a gift of $100,000 at their twenty-fifth reunion. There are 50 in the class and they can invest at 8 percent. They plan to start out giving a small amount at the end of the first year and in- crease their gifts to the class fund by 10 percent each year. Find the amount each graduate would donate at the end of the first year in order to reach their class goal of $100,000 at the end of 25 years. (Ans. C= $10.03)

Remember to illustrate diagramatically for some of these parts! 6. Assume you can work as many hours you wish at £12 per hour (net of tax). If you do not work, you have no income. You have no ability to borrow or lend, so your consumption, c, is simply equal to your income. a) Derive and plot the feasible set, between daily values of consumption c, and “leisure”, l.  Label the values at the intercepts (the points where the feasible frontier cuts the two axes). b) Assume that your optimal choice of consumption and leisure is to work 8 hours per day. Illustrate this choice diagrammatically using the feasible set and indifference curves. c) Use indifference curves and the feasible set to show why, given the properties of the optimal choice in part b), it is not optimal to work, say, 10, or 6 hours per day. d) Now assume that you receive an income of £140 per week from an unknown benefactor. Show the impact on your feasible set, and show a new optimal choice in which consumption increases…

1. Someone is willing to maximize his/her utility. Assume he/she knows his/her u(x,y) =x^0,5y^0,5 (Cobb-Douglas) (a) Find his/her optimal consumption given the income = 20, Px=2, Py=4! (b) Depict his/her optimal consumption graph! 2. Suppose that x and y (from your answer in number 1) are now perfect complement with u(x,y) = min(x,y). (a) Find his/her optimal consumption (given the same income and prices)! (b) Depict his/her optimal consumption graph!

3) Marco has $100 worth of grain in period 1 but gets no grain in period 2. Marco has two choices. He can store the grain that he does not consume in period 1. This results in a loss of 20% of the grain due to pests. Assume that with this option he will choose to consume 68 units of grain in period 1 and 26 units in period 2. Instead, Marco can sell the grain he does not consume in period 1 and lend the money from that sale to someone today at an interest rate of 10%. He can then use the repayment of that loan to buy gain in period 2. a) Based on this information, draw a diagram that outlines Marco's choices. Is he definitely better off once the opportunity to lend is available to him? b) Relative to his initial equilibrium point, does he unambiguously consume more in both periods once he can lend out the excess he does not consume in period 1? c) Now assume that Marco can sell any excess grain he doesn't consume in period 1 and invest the money he gets in a new type of risky activity.…