Answer to Question #234985 in Microeconomics for Daakyehene

Question

Suppose the market for corn in Ghana is described by the following demand and supply equations:

Demand: P = 100 – (1/2)Q

Supply: P = 10 + (13/10)Q.

Where, P is price(₵/bag); and, Q is quantity(bags). Use this information to answer the

following questions.

       

a. What is the equilibrium price and quantity of corn in this market? (5 marks)

b. Plot the demand and supply of corn and show the intercept values, equilibrium quantity

and price. (10 marks)

c. What is the total revenue derived in this market? (5 marks)

d. Suppose the government institutes a price support of ₵80 per bag of corn.

i. How many bags of corn should the government buy to maintain this price? (5 marks)

ii. What is the cost of this program to government if storage costs is ₵10 perbag? 

Answer 1

a

Market equilibrium occurs where the demand function and supply functions intersect

dd=ss

Demand: P = 100 – $(\frac{1}{2}\times Q)$

Supply: P = 10 + $(\frac{13}{10} \times Q)$

Therefore equilibrium is

100 – $(\frac{1}{2}\times Q)$ = 10 + $(\frac{13}{10} \times Q)$

Rearranging the equation and multiplying both sides by 10 we get

900 =5Q +13Q

900 = 18Q then dividing both sides by 18

Q= 50 UNITS Equilibrium quantity

Substituting Q into the supply or demand function

p = 10 + $(\frac{13}{10} \times 50)$

p = 75 equilibrium price

b

c.

Total revenue = P$\times Q$

Total revenue = 75 $\times 50$

TR= 3750

d

i.

New price per bag = 80

The government then faces a similar demand function

Demand: P = 100 – $(\frac{1}{2}\times Q)$

If it set P =80 the Q will be calculated as follows;

80 = 100 – $(\frac{1}{2}\times Q)$ rearranging and multiplying by 2 both sides we get

-40=-Q

Hence Q = 40

ii

storage cost of one bag = 10

Then storage cost of 40 bags will be

40 $\times$ 10 = 400