Answer to Question #252350 in Microeconomics for pragati

Question

Q1. In Arthnagar, the demand function of wheat is estimated as: QD = 100-5P The supply function of wheat is estimated to be: Qs = -32+6P Where QD and Qs are respectively, the quantities demanded and supplied and P is the prevailing market price (expressed in Rs per Kg). Assuming that the wheat market is competitive, answer the following questions: 1. What is the quantity of wheat bought when it is offered free of charge? What is the maximum price which consumers of Arthnagar are willing to pay for wheat?What is the minimum price at which producers are induced to supply wheat? 4. What is the equilibrium market outcome? Determine the consumers’ and producers’ surplus at the equilibrium market outcome. A tax of Rs 11 per Kg is levied on wheat by the Arthnagar Panchayat. How would the same alter the equilibrium outcome? Now assume that the wheat is supplied by a monopolist who can indulge in perfect price discrimination. Compare the current equilibrium outcome to that of the competitive market

Answer 1

(1)

$Q_D=100-5P$

Quantity bought when wheat is offered free of charge is:

$Q_D=100-5(0)$

$=100$

(2)

$Q_D=100-5P$

$100-5P=0$

$P=20$

(3)

$Q_S=-32+6P$

$-32+6P=0$

$P=5.33$

(4)

At equilibrium, $Q_D=Q_S$

$100-5P=-32+6P$

$P=12$

$Q=100-5(12)$

$Q_E=40.$

(5)

Consumer surplus = 1/2 *(Quantity bought) *(maximum price- actual price paid).

$=\frac{1}{2}\times 40\times(20-12)=180$

Producer surplus =1/2*(Quantity sold)*(Actual price- minimum price to sell)

$=\frac{1}{2}\times40\times(12-5.33)= 133.4$