Question

1. Olivia likes to eat both apples and bananas. At the grocery store, each apple costs $0.20 and each banana cost $0.25. Olivia’s utility function for apples and bananas is given by U(A, B) = 6 (AB)1/2 . If Olivia has $4 to spend on apples and bananas, how many of each should she buy to maximize her satisfaction?

Use the tangency condition to find the optimal amount of A to relative to B .

MUA/PA = MUB/PB

Now plug this into the budget constraint to find the optimal amount of B to purchase.

Finally, plug this result into the relationship between A and B above (that we found using the tangency condition) to determine the optimal amount of A ; A =1.25(8) =10 .

Therefore, she should buy 10 apples and 8 bananas to maximize her utility.

2. A consumer purchases two goods, food (F) and clothing (C) . Her utility function is given by

U(F,C) = FC + F . The price of food is PF , the price of clothing is PC , and the consumer’s income is I.

a) What is the equation for the demand curve for clothing?

b) Is clothing a normal or inferior good in this case?

Setting up the tangency condition implies

Substituting this result into the budget line implies

Since the amount of clothing purchased will increase as income increases, as noted by the

demand curve, clothing is a normal good, and not an inferior good

3. Consider the following information:

• Jessica’s utility function is U(x, y) = xy.
• Maria’s utility function is U(x, y) = 1,000xy.
• Nancy’s utility function is U(x,y) = -xy.
• Chawki’s utility function is U(x,y) = xy - 10,000.
• Marwan’s utility function is U(x,y)= x(y + 1).

Which of these persons have the same preferences as Jessica?

3. Suppose the market demand for a product is given by

Q^d = 1000 −10P

     and the market supply is given by

Q^s= −50 + 25P

1. What are the equilibrium price and quantity?
2. Calculate the Consumer Surplus.
3. At the market equilibrium, what is the price elasticity of demand? Is demand elastic, unitary elastic or inelastic?
4. Suppose the price in this market is $25. What is the amount of excess demand?

4. The following conversation was heard among four economists discussing whether the minimum wage should be increased:

Economist A. “Increasing the minimum wage would reduce unemployment of minority teenagers.”

Economist B. “Increasing the minimum wage would present an unwarranted interference with private relations between workers and their employers.”

Economist C. “Increasing the minimum wage would raise the incomes of some unskilled workers.”

Economist D. “Increasing the minimum wage would benefit higher-wage workers and would probably be supported by organized labor.”

Which of these economists are using positive analysis and which are using normative analysis in arriving at their conclusions? Which of these predictions might be tested with empirical data? How might such tests be conducted?

5. If production function is given by Q = KL, what would happen when both inputs double.

6. The production function is given by Q = K^1/3L²,

a. Determine the marginal product of capital, MP_k?

b. Does the law of diminishing marginal productivity apply for capital use?

7. Suppose MP_L = 20 and MP_K = 40 and the rental rate on capital is $10. If the level of production is currently efficient, what should the wage rate be?

Answer 1

The price of apple Pa= $0.20

The price of banana. Pb= $0.25

The budget of the consumer= $4

The budget constraint becomes:

0.20A+0.25B= 4

The utility function is:

U= 6AB/2= 3AB

The marginal utility of A, MUa

The marginal utility of B. MUb,

From the optimality condition:

MUA/PA = MUB/PB

3B/0.20= 3A/0.25

A/B= 0.25/0.20= 5/4

A=5B/4

Putting this value in the budget constraint,

0.20A+0.25B= 4

0.20(5B/4) +0.25B= 4

0.5B= 4

B= 8

, Thus, A= 5*8/4= 10