2. (5 marks) Consider the market model: Qs = 4P - 3 QD = -2P + 13 dP dt Where Qs = quantity supplied; QD = quantity demanded and P = price. Determine the following: (a) If P(0) = 2, find an expression for P(t) by solving the differential equation. (b) Find an expression for Qs(t) and QD (t). (c) Is this system stable or unstable? Explain. = 0.4(QD - Qs)

When sold for $790.00, a certain desktop has an annual supply of 129.5 million computers and an annual demand of 155.5 million computers. When the price increases to $865.00, the annual supply increases to 147.5 million computers, and the demand drops to 134.5 million computers. NOTE: Round slope and vertical intercept to 4 decimal places and use those rounded values to the end. (a) Assuming that the supply and demand equations are linear, find the supply and demand equations. Supply Equation p = Demand Equation p = esc (Note: The equations should be in the form p = mq + b where p denotes the price (in dollars) and q denotes the quantity (in billions). The slope and y-intercept should be accurate to 4 decimal places). (b) Find the Equilibrium price and quantity. Equilibrium price p = Equilibrium quantity q = 9- F2 A (Note: The equilibrium price should be accurate to 2 decimal places and quantity should be rounded to the nearest whole number, and the equilibrium price should include a…

2) Daniel has the following Jineas Preferences over black tea be) and milk (y) (a) Setup the expenolituse minmization Problem for Daniel. what conditions, (BC) or(NNC) will necessarily be (b) Solve the expenditure Problem and obtain the Compensated and the Cost minimization function when binding at the oPtimum? ū = 40 and P = $6. c) Other Pic attach for Part(c)

(a) Determine the equilibrium price and quantity.(b) Sketch the demand and supply functions on the same graph. Label theaxes and the intercepts clearly.

1. Suppose consumers will demand 40 units of product when the price is $12 and 25 units when the price is $18 each. 6). Find a linear equation for the: 0. Demand curve. (ii). Demand function. (b). Find the price per unit when 30 units are demanded. 2 The demand Curve for a prodtuct is p= 60-0.00OSC where p iE the price per unit. and q is the number of units demancec. How many units must be sold to achieve sales of $1.200,000?

The quantity of hot dogs buns demanded at a price of $1.59 increased from 100units to 130unite during the week that hot dogs went on sales for $1.89 rather than the regular price of $2.59. (a) what data points (P1 Q1) (P1 Q2) would you use to calculate the cross elasticity of demand for hot dogs and buns? (b) would the cross elasticity of demand be positive, zero or negative? What does this represent in economics terms? (c) the next time hot dogs went on sales, the price of buns was increased to $1.79 and only 120 buns was sold. Was this a good business decision? Why/why not?

The quantity demanded each month of Russo Espresso Makers is 250 when the unit price is $140. The quantity demanded each month is 1000 when the unit price is $110. The suppliers will market 750 espresso makers when the unit price is $76 or higher. At a unit price of $96, they are willing to market 2250 units. Both the supply and demand equations are known to be linear. (a) Find the demand equation. P = (b) Find the supply equation. p= (c) Find the equilibrium quantity and the equilibrium price. units $

The manager of a Cape Town superette carries a stock of Jive soft drinks. The countryexperiences an economic recession which yields an anticipated consumer income decrease of6 %. As a result, the income elasticity of demand for this product is estimated to be –2.5.(a) Calculate the percentage change in the quantity of your soft drink orders required toaccommodate the new demand without a surplus or shortage of inventory. [3](b) What does the elasticity coefficient of –2.5 reveal? [3]

Subpart to be solved 1. Consider the following: If the price per unit of good A is P200 quantity purchased isvalued at 1,500 units. If price changes (increase or decrease) by P1, quantity demandedchanges (decreases or increases) by 4 units.A. Determine the demand function expressed as a price function. B. Set up a demand schedule for this function and determine the price elasticity ofdemand at various P and Qd combinations using point-price elasticity formula.(Make sure that all elasticity concepts are found on the same demand curve.) C. Determine the TR and MR functions.D. Graph the demand curve and the TR curve (TR curve just below the demand curve)E. At what P and Qd combination will TR be maximum?

Q1 The market demand and supply functions of a good are given by: QD = 400 – 15P Qs =-50 + 10P where QD, Qs and P denote quantity demanded, quantity supplied and price, respectively. (a) Work out the values of QD and Qs when P = 5, 10, 15, 20 and 25, and hence draw accurate graphs of the demand and supply curves on the same diagram with Q plotted on the horizontal axis and P plotted on the vertical axis. (b) Hence, or otherwise, find the equilibrium price and quantity. (c) For what values of P is there excess demand? (d) The government decides to impose a fixed tax of $5 on each good. Describe the effect, if any, on the demand and supply curves on your diagram and calculate the new equilibrium price and quantity.