Question

Consider the details of good 'x' given and answer the questions below. Use illustrations to explain your answer, where appropriate. a. Do you "Agree" or "Disagree" with the following? Explain your answers. Price (Rs.) 12 20 Quantity demanded (Units) 120 40 Quantity supplied (Units) 20 140 i. The Price Elasticity of Demand for fuel is more elastic in the long run. ii. The broader the definition of a commodity, the lower its Price Elasticity tends to be. iii. The higher the substitutability of products, higher the Cross Price Elasticity iv. The lower the cost of production, the higher is the Price Elasticity of supply. (12 Marks) b. The demand for product 'x', given as, i. ii. iii. Develop the demand and supply equations, of good 'x'. Find the price and quantity of good 'x' at equilibrium point. Calculate the Price Elasticity of Demand and Supply at the equilibrium price. Comment on the elasticity coefficients. If the government imposed a tax of Rs. 3/= on every unit that is being supplied, find the new equilibrium price and quantity. How is the tax shared between consumers and suppliers? Is there a relationship between how the tax is shared between the two parties and elasticities, calculated in part (iii)? Explain. Qx = 3176 - 20PX +0.21 - 16P, Price of good (x) Price of related good (y) Income per capita (1) = Rs.247= = Rs.36/= = Rs.20,000/= i. ii. iii. Find the quantity demanded of good 'x', at initial prices and income. To increase the revenue earned from good 'x', should the price of 'x' be increased or decreased? Explain. How would the sale of good 'x' change during the period of rising and declining income? What is the nature of relationship between good 'x' and 'y? If the objective is to maintain the quantity of good 'x' demanded as computed in part (i), how would the price of 'x' be changed to compensate for Rs. 12/= increase in price of y. iv.

Answer 1

(First Question)

(i)

(A) Demand equation: Q = a - bP

Using table,

120 = a - 12b.......(1)

40 = a - 20b.......(2)

(1) - (2) gives

8b = 80

b = 10

a = 40 + 20b [from (2)] = 40 + 20 x 10 = 40 + 200 = 240

Demand: Q = 240 - 10P

(B) Supply equation: Q = c + dP

Using table,

20 = c + 12d.........(3)

140 = c + 20d.........(4)

(4) - (3) gives

8d = 120

d = 15

c = 20 - 12d [from (30] = 20 - 12 x 15 = 20 - 180 = - 160

Supply: Q = - 160 + 15P

(ii)

Setting demand = supply

240 - 10P = - 160 + 15P

25P = 400

P = 16

Q = 240 - 10 x 16 = 240 - 160 = 80

(iii)

Using demand equation: Elasticity of demand (Ed) = (dQ/dP) x (P/Q) = - 10 x (16/80) = - 2

Using supply equation: Elasticity of supply (Es) = (dQ/dP) x (P/Q) = 15 x (16/80) = 3

(iv)

After tax, new supply curve is:

Q = - 160 + 15 x (P - 3) = - 160 + 15P - 45 = - 205 + 15P

Setting demand = new supply,

240 - 10P = - 205 + 15P

25P = 445

P = 17.8 (price paid by buyers)

Price received by sellers = 17.8 - 3 = 14.8

Q = 240 - 10 x 17.8 = 240 - 178 = 62

Tax burden of buyers = price paid by buyers - pre-tax price = 17.8 - 16 = 1.8

Tax burden of sellers = 3 - 1.8 = 1.2

Since absolute value of Ed is lower than the value of Es (2 < 3), tax burden of buyers is less than that of sellers.

NOTE: As HOMEWORKLIB's Policy, 1st question is answered.