Question

9. Calculate the cross-price elasticites in the case of a decrease in the price of cabbage at 20%, an increase in the demand of tomatoes at 15% and a decrease in the demand of artichokes at 10%. Comment on whether tomatoes and articokes are substitutes for or complements with cabbage.

13. Represent a demand function with QD = 6 - P

a. Graph the demand function (with intercepts on the horizontal and vertical axes).

b. If the price equals 2 (dollars), what is the consumer surplus?

c. If the price increases to 4 (dollars), what is the new value of the consumer surplus? This new value should be lower, and please explain why this should be true.

Answer 1

Solution:

9. Cross price elasticity = percentage change in quantity demanded of a good/percentage change in price of related good

Then, cross price elasticity of demand for tomatoes = 15/(-20) = -0.75

And that for artichokes is = (-10)/(-20) = +0.50

Since, the cross price elasticity for tomatoes is negative, tomatoes and cabbage can be said as complements. This is because: with decrease in price of cabbage, and law of demand states that this should result in increase in demand for cabbage. Only if both are consumed together, an increase in demand for cabbage will increase demand for tomatoes as well.

With similar reasoning, we can say that artichokes and cabbage are substitutes as the cross price elasticity is positive.

13. Given the demand function: Qd = 6 - P:

a) This can be graphed with intercepts at 6, that is with price on vertical axis, price intercept is (0, 6) and quantity on horizontal axis, quantity intercept is (6, 0). Following is the required graph:

b) When price = 2, quantity demanded = 6 - 2 = 4 units

Consumer surplus = area of triangle above price line and below the demand curve, so

CS = (1/2)*quantity demanded*(maximum payable price - price paid) [This can be seen graphically as well, with (horizontal) price line at $2]

CS = (1/2)*4*(6 - 2) = $8

c) When price increases to $4, new quantity = 6 - 4= 2 units

So, new consumer surplus = (1/2)*2*(6 - 4) = $2

Clearly, this new value of surplus is lower ( 2 < 8), as with a higher price, there are two effects: firstly, consumers are able to buy lesser than before, and secondly, for each unit bought they have to pay a higher price, and so saving from maximum willingness to pay is lower.