Consider the following situations. In the table, (Px, Py, M) describes the prices and income and (x, y) describes the chosen bundle under those prices and income. Situation Prices and Income Chosen bundle 1 2 3 (b) O (2,4,10) (1,8,5) (4,2,6) A = (1,2) B = (1,0.5) C = (1,1) Which bundles amongst the 3 chosen ones is A directly revealed preferred to? Which bundles amongst the 3 chosen ones is B directly revealed preferred to? Which bundles amongst the 3 chosen ones is C directly revealed preferred to?
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- Define the following: i) Simple interest. ii) Breakeven point. iii) Ordinary annuity. b) When the price of a commodity is Sh. 530 the unit demand is 55 units. The demand is 120 units when the price is Sh. 270. If the cost of production is C = 2q + 150, Calculate the profit when 5 units are produced and sold. c) The present value of an annuity due is Sh. 284,000 after 4 years at a discount rate of 10%. Calculate the annual payment. d) A man deposits Sh. 12,000 in a bank at the beginning of each year. The compound interest is 12% per year. Calculate how long it will take for an accumulated amount of Sh. 95,000.Question 4 A consumer is maximising her utility function: U (x, y) = (205 + y05)², subject to the budget constraint 4x + 2y 108. (a) Set up the Lagrangian function of this utility maximisation problem and derive the first-order conditions. (b) What are the utility maximizing amounts of x and y? Also, calculate the Lagrange multiplier. (c) What are the utility maximising amounts of x and y if the budget constraint changes to x + 2y = 36? How would A change? Explain your reasoning. (Hint: You do not need to calculate A, rather comment on how it would change and why.)(Marginal Analysis). A retailer has determined that the monthly sales of a watch are 150 units when the price is $50, but decrease to 120 units when the price is $60. Assume that the demand is a linear function of the price. (4a) Find the demand as a linear function of the price (4b) Find the revenue R as a function of x (4c) Approximate the change in revenue for a one-unit increase in sales when x = 141
- 2. Supose that a consumer has utility function U with U (₁,22) = x1426, where ₁ and ₂ are demand of commodity 1 and 2. Suppose that the price of commodity 1 and 2 is $3 and $5, respectively. This consumer has money m = 12 to spend and wants to maximize utility with constraint the money. (a) Write the Lagrangian function. (b) Find the critical point using first order condition. (c) Find the Hessian matrix to check whether the critical point is maximiser or minimiser. (d) Find the maximum utility.11- It is estimated that consumers will buy Q (p) 4,374 kg of imported beans per week when p2 the price is p$ per kg. It is estimated that t weeks from now, the price of this type of beans will be p(t) = 0.04t2 + 0.2t + 12 dollars per kg. a. Estimate the weekly consumer demand for the beans as a function of t. b. How many kg of beans will consumers buy 10 weeks from now?Consider the utility function uu(xx, yy) 10 for all bundles (xx, yy) (a) What are strict preferences? What are the indifferences? (b) Argue that the preferences represented by this utility function are strictly convex or that they are not. (c) Árgue that the preferences represented by this utility function are complete or that they are not. (d) Argue that the preferences represented by this utility function are strongly monotonic or they are not.
- suppose that a consumer has a utility function U(x,y) = x1/3 y2/3 At the point (x,y) = (4,7) in order to keep utility the same and get one more unit of x, the consumer would be willing to give up how many units of y ? (a) 7/4 (b) 4/7 (c) 7/8 (d) 4/14The owners of a small manufacturing concern have hired a vice president to run the company with the expectation that he will buy the company after five years. Compensation of the new vice president is a flat salary plus 75% of the first $150,000 profit, and then 10% of profit over $150,000. Purchase price for the company is set at 4.5 times earnings (profit), computed as average annual profitability over the next five years. a. Plot the annual compensation of the vice president as a function of annual profit. b. Assume the company will be worth $10 million in five years. Plot the profit of buying the company as a function of annual profit. c. Does this contract align the incentives of the new vice president with the profitability goals of the owners? d. Redesign the contract to better align the incentives of the new vice president with the profitability goals of the owners.What is the 4p ( Product, price, place, promotion) of caribou coffee ?
- Q2/suppose there were six kinds of toppings that one could order for a pizza. How many combinations of exactly 3 toppings could be ordered?(a-) Given the function , y = 4x2 + 9 - Eind the derivative dy/dx.2 3) For each utility function, determine the marginal utility with respect to x, marginal utility with respect to y, and the MRS. (3pts each) a) U(x, y)-3x+2y b) U(x, y) 10x¹/5 y c) U(x, y)=x+ y²