Question

A consumer has a total budget of $200. There are two (2) goods that are preferred by the consumer, organic apples and organic bananas. Organic apples retail for $10 per pound and the organic bananas retail for $5 per pound.

a. Derive the Budget constraint equation based on the data above.

b. Discuss (use of graph is not required, given the limitation here), the income and substitution effects of a price change, if the price of apples is reduced by 50%. In other words, how is the consumer better or worse off as a result of the price change, with specific reference to the concepts of income and substitution effects.

c. If you are told that following the 50% price reduction in apples, the quantity of apples consumed increases from 500 to 750 units, calculate the point price elasticity of demand. Discuss the significance of the value of the point elasticity calculated.

d. How would the answer derived in part (c) affect the revenues of the firm?

Answer 1

A. Budget constraint equation

Px. Qx +Py.Qy =M

suppose the organic apple is X and banana is Y. Then the equation will be

10x. Qx + 5y. Qy =200.......(1)

If Qx = 0, Qy = M/Py

200/5 = 40

If Qy =0 , Qx = M/Px

200/10 =20

B. (a) Price effect

Price effect means when the price of one commodity ( apple ) falls, it become relatively cheaper than the other(banana). The consumers have a tendency to substitute cheaper goods for relatively costlier one.

(b) Income effect

It means fall in the price of apply increases consumer's real income. Change in real income causes a change in the consumers consumption habit.

This can be shown in the following diagram

If the price of apply falls to 50% that is price falls from 10 pound to 5 pound the price line shifts from LM to LM1. and new equilibrium point is established at B where IC1 tangent to the new budget line.

Price effect = Substitution effect (SE) and income effect(IE)

Suppose, When govt imposes tax on income, income line shifts back to L1M* which tangent the first IC curve and a new equilibrium point is established at point C.

Price effect = X X* +X*X1

In short price of apple falls to 5, consumers can purchase more apple than banana.

C. Point elasticity of demand shows the price elasticity of demand at a specific point on a demand curve. Here

This can be calculated as

PED = delta Q /delta P * P/Q

250/5*10/500 =1

elasticity of demand at the centre point. Which means if price changes demand changes in the same proportion.

D. If e =1, the firm's total revenue remains the same because if price increases quantity also increases in n the same proportion.