Question

Instructions: Please write your answers in the spaces provided below. Show all work on the blank pages you were given for partial credit. Please write your name on all pages submit ted and staple them together 1. The demand and supply functions for a good are given as (1)Demand function: Pd 50 3Qd (2)Supply function: Ps141.5Qs a. Calculate the equilibrium price and quantity algebraically b. What is the Quantity Demanded when Price is zero? The Quantity Supplied? Interpret your results c. Now suppose the government imposes a $20 price on this good. Is this a PRICE CEILING or a PRICE FLOOR? d. What are the new values of d and Qs after the government's intervention? e. Describe the type of market disequilibrium which results from the gover nment's intervention. What is the magnitude of this disequilibriun? f. Is a black market possible for this good? Explain why or why not. 2. Suppose the price of a good is set such that Price $6 for every unit sold The firm faces fixed costs equal to $90 and per-unit costs of $3 a. State the Total Revenue (TR) function b. State the Total Cost (TC) function c. State the Profit function d. What is the quantity of the good produced at the breakeven point? e. What are the values of TR and TC at the breakeven point? 3. A firm's Total Cost function is given by the equation TC 200 + 3Q นใ ile the demand function it faces is P 107-2Q a. State the Total Revenue function b. State the Profit function c. For what values is Profit equal to zero? (Hint: Find the roots) where P is Price and Q is Quantity. The subscripts indicate the corresponding function

Answer 1

1.

a) At Equilibrium Pd will be same as Ps and Qs will be same as Qd

So 50- 3Q= 14 + 1.5Q

Or 4.5Q= 36, Or Q = 36/4.5 = 8 units

Price will be 50- 3*8 = 50-24 = $26

b) At Pd = 0, 50- 3Qd= 0, or Qd = 50/3 which is equivalent to 17 units

Quantity supplied at Ps = 0 or 14 + 1.5Qs= 0, Qs= -14/1.5 which is equivalent to -10

Interpretation: Sellers will not sell product at Price = 0, because they have fixed cost which will not recover at price = 0

c)$20 is a Price Celing at it is the maximum price set by governemnt at which product could be sold.

d) At Price = $20,

Qd= (50-20)/3= 10, Qs= (20-14)/1.5= 4

e) Such Government intervention will increase demand of good and decrease supply of good as price set is below equilibrium price. As calculated in point d), supply of good will be 6 units lesser than demand of good(4 units supply in comparision to 10 units demand)

f) Yes, black market is possible for this good. Seller could charge higher price than controlled price illegally as demand of good is more than supply of good at current price.

2.

a) Total Revenue function is 6Q (Price into total units sold)

b) Total Cost function will be 90 + 3Q (Fixed cost +Quantity X PEr unit Variable Cost)

c) Profit Function is TR-TC which will be 6Q - 90 - 3Q = 3Q-90

d) At Breakeven, Proit Function will be equal to 0

Or 3Q-90 = 0, Or Q =30. Hence the company will breakeven by selling 30 units

e) At Breakeven, TR= 6X30= 180, TC= 90 + 3*30= 180. Hence, both are same.

3. Demand Function or Price = 107- 2Q

TC= 200+ 3Q

a) Total Revenue = Price X Quantity = 107Q - 2Q^2

b) Profit function is TR - TC, OR 107Q - 2Q^2 - 200 - 3Q Or 104Q- 2Q^2 - 200

c) For Profit =0, 104Q - 2Q^2 - 200 = 0 Or 2Q^2 - 104Q + 200 = 0

Or Q^2 -52Q + 100 = 0

Or (Q-2)(Q-50)= 0

Or Q= 2 Or Q=50

Thanks