Answer to Question #256386 in Microeconomics for Dhananjay

Question

Q.) Assume a consumer has $40 to spend and for both products the marginal utilities are shown in the following table: Quantity. MU A. MU B 1. 35 80 2. 20 40 3. 12 18 Assume that each product sells for $10 per unit. A.) How many units of each product will the consumer purchase? B.) Assume the price of product B rises to $20 per unit. How will this consumer allocate her budget now? C.) If the price of both products rise to $20 per unit , what will be the budget allocation?

Answer 1

Solution:

A.). Utility maximizing quantity is where: MU_A/P_A = MU_B/P_B

Budget constraint: I = P_AA + P_BB

40 = 10A + 10B

40 = (10 $\times$ 2) + (10 $\times$ 2)

40 = 20 + 20

40 = 40

To maximize utility, the consumer will purchase 2 units of product A and 2 units of product B.

Product A = 2 units

Product B = 2 units

 

B.). The new budget constraint: 40 = 10A + 20B

To maximize utility, the consumer will now purchase 2 units of product A and 1 unit of product B.

Product A = 2 units

Product B = 1 unit

40 = 10A + 20B

40 = (10 $\times$ 2) + (20 $\times$ 1)

40 = 20 + 20

40 = 40

 

C.). New budget constraint = 40 = 20A + 20B

To maximize utility, the consumer will now purchase 1 unit of product A and 1 unit of product B.

Product A = 1 unit

Product B = 1 unit

40 = 20A + 20B

40 = (20 $\times$ 1) + (20 $\times$ 1)

40 = 20 + 20

40 = 40