# Budget Set, Normal and Inferior Goods

Managerial Economics and Business Strategy by Baye.

Chapter 4 #6, 9 solution answer

6) In the following figure, a consumer is initially in equilibrium at point C. The consumer's income is $400, and the budget line through point C is given by $400 = $100X + $200Y. When the consumer is given a $100 gift certificate that is good only at store X, she moves to a new equilibrium at point D. (pdf file of figure is attached).

a. Determine the prices of goods X and Y.

b. How many units of product Y could be purchased at point A?

c. How many units of product X could be purchased at point E?

d. How many units of product X could be purchased at point B?

e. How many units of product X could be purchased at point F?

f. Based on this consumer's preferences, rank bundles A, B, C, and D in order from most preferred to least preferred.

g. Is product X a normal or an inferior good?

9) A consumer's budget set for two goods (X and Y) is 600 ≥ 3X + 6Y.

a. Illustrate the budget set in a diagram.

b. Does the budget set change if the prices of both goods double and the consumer's income also doubles? Explain.

c. Given the equation for the budget set, can you determine the prices of the two goods? The consumer's income? Explain.

https://brainmass.com/economics/managerial-economics/budget-set-normal-inferior-goods-581875

#### Solution Preview

Please refer to the 3 pdf files attached for the complete solutions. Only the text portions of the files have been provided here.

6a) In the following formula, is the price of X and is the price of Y.

Compare the formula with the budget line to determine the prices of X and Y. The price of good X is $100 and the price of good Y is $200.

b) The number of units of product Y that could be purchased at point A can be found using . Substitute $400 for M and $200 for

2 units of product Y could be purchased at point A.

c) The number of units of product X that could be purchased at point E can be found ...

#### Solution Summary

This solution includes detailed explanations and step-by-step calculations for the 2 problems in 3 pdf files. The solution to #6 includes over 450 words. The solution to #9 includes over 150 words, and a figure.

Managerial Economics - Set of multiple choice questions.

5. Suppose total benefits and total costs are given by B(Y) = 100Y-8Y(squared) and C(Y)=10Y(squared). What is the maximum level of net benefits?

A. 92 B. 139 C. 78 D. None of the above

8. Which of the following is the incorrect statement?

A. The marginal benefits curve is the slope of the total benefits curve

B. dB(Q)/dQ = MB

C. The slope of the net benefit curve is horizontal where MB = MC

D. The difference in the slope of the total benefit curve and the total cost curve is maximized at the optimal level of Q.

9. Trade will take place:

A. If the maximum that a consumer is willing and able to pay is less than the minimum price the producer is willing and able to accept for a good.

B. If the maximum that a consumer is willing and able to pay is greater than the minimum price the producer is willing and able to accept for a good

C. Only if the maximum that a consumer is willing and able to pay is equal to the minimum price the producer is willing and able to accept for a good

D. None of the above.

11. In a competitive market, the market demand is Qd(demand) = 60- 6P and the market supply is Qs(supply) = 4P. The full economic price under a price ceiling of $3 is:

A. 6 B. 7 C. 8 D. 9

14. Suppose market demand and supply are given by Qd = 100-2P and Qs =5+3P. If a price ceiling of $15 is imposed, what will be the resulting full economic price?

A. $19 B. $21 C. $6 D. $25

15. Suppose market demand and supply are given by Qd = 100-2P and Qs =5 + 3P. If the Government sets a price floor of $30 and agrees to purchase all surplus at $30 per unit, the total cost to the Government will be:

A. $1,650 B. $1,375 C. $900 D. $1,125

16. Suppose the supply increases and demand decreases. What effect will this have on price and quantity?

A. Price will increase and quantity may rise or fall

B. Price will decrease and quantity will increase

C. Price will decrease and quantity will decrease

D. None of the above

17. Suppose the demand for X is given by Qxd = 100-2Px + 4Py + 10M + 2A, where Px represents the price of good X, Py is the price of good Y, M is income and A is the amount of advertising on good X. Based on this information, we know that good X is:

A. A substitute for good Y and a normal good.

B. A complement for good Y and an inferior good.

C. A complement for good Y and a normal good.

D. A substitute for good Y and an inferior good.

21. The demand for good X has been estimated by Qxd = 12 - 3Px + 4Py. Suppose that good X sells at $2 per unit and good Y sells for $1 per unit. Calculate the own price elasticity.

A. -0.2 B. -0.3 C. -0.4 D. -0.5 E. -0.6

23. If the income elasticity for lobster is .4, a 40% increase in income will lead to a :

A. 10% drop in demand for lobster B. 16% increase in demand for lobster

C. 20% increase in demand for lobster D. 4% increase in demand for lobster

24. Suppose the demand function is given by Qxd = 8Px(to the .5), Py(to the .5), M(to the .12) H. Then the demand for good X is:

A. Inelastic B. Unitary C. Elastic D. Perfectly elastic

29. The management of Local Cinema has estimated the monthly demand for tickets to be log Q = 22,328 - .41 log P + 0.5 log M - .33 log A + log Pvcr, where Q = quantity of tickets demanded, P = price per ticket, M = income, A = advertising outlay, and Pvcr = price of a VCR tape rental. It is known that P = $5.50, M = $9,000, A = $900, and Pvcr = $3.00. Determine the own-price elasticity of demand for movie tickets.

A. -.29 B. -.32 C. -.39 D. -.41

30. If the demand function for a particular good is Q = 20 - 8P, then the price elasticity of demand (in absoulte value) at a price of $1 is:

A. 8 B. 2 C. 2/3 D. 1/8 E. None of the above

31. Joe prefers a three pack of beer to a six pack. What properties does this preference violate?

A. Completeness B. Transitivity C. More is better D. Diminishing MRS

36. At the equilibrium consumption bundle, which of the following holds?

A. MRSx,y=Px/Py B. MRSx,y= -Px/Py C. MRSx,y= -Py/Px D. MRSx,y=Py/Px

37. Suppose a worker is offered a wage of $8 per hour, plus a fixed payment of $100 per day, and he can use 24 hours per day. What is the equation for the workers opportunity set? (E is total earnings and L is leisure).

A. E=100-8L B. E=192-8L C. E=292-8L D. None of the above

38. The revenues earned by the firm from the consumer may be maximized under:

A The regular price offer B. The buy one get one free C 50% discount D. 40% discount

39. If sugar and Nutrasweet are substitutes, then we can be certain that a decrease in the price of sugar will lead to:

A. An increase in the consumption of Nutrasweet.

B. An increase in the consumption of sugar.

C. An increase in the consumption of sugar and Nutrasweet.

D. None of the above.

41. For the cost function C(Q) = 100 + 2Q + 3Q(squared), the marginal cost of producing 2 units of output is

A. 2 B. 3 C. 12 D. 14

43. Which of the following conditions is true when a producer minimizes the cost of producing a given level of output?

A. The MRTS is equal to the ratio of input prices.

B. The marginal product per dollar spent on all inputs are equal.

C. The marginal products of all inputs are equal.

D. A and B

44. The production function for a competitive firm is Q = K(to the .5)L(to the .5). The firm sell its output at a price of $10, and can hire labor at a wage rate of $5. Capital is fixed at one unit. The profit-maximizing quantity of labor is:

A. 2/5 B. 1 C. 10 D. None of the above

45. Total product begins to fall when:

A. Marginal product is maximized B. Average product is below zero.

C. Average product is negative D. Marginal product is zero.

50. Two firms producing identical products may merge due to the existence of:

A. Economies of scope B. Economies of scale

C. Cost complementarity D. All of the above E. A and C only

2. The supply function for good X is given by Qxs = 1000 + Px-5Py-2Pw, where Px is the price of X, Py is the price of good Y, and Pw is the price of input W. If the price of input W increases by $10, then the supply of good X:

A. Will increase by 10 units. B. Will increase by 20 units

C. Will decrease by 10 units. C. None of the above

3. The cross-price elasticity of demand for textbooks and copies of old exams is -3.5. If the price of copies of old exams increase by 10%, the quantity demanded of textbooks will:

A. Fall by 3.5% B. Rise by 3.5% C. Fall by 35% D. Rise by 35%

4. Mitchell's money income is $150, the price of X is $2, and the price of Y is $2. Given these prices and income, Mitchell buys 50 units of X and 25 units of Y. Call this combination of X and Y bundle J. At bundle J, Mitchell's MRS is 2. At bundle J, if Mitchell increases consumption of Y by 1 unit, how many units of X must he give up in order to satisfy his budget constraint?

A. 1/ B. 1 C. 2 D. 4

5. For the cost function C(Q) = 1000 + 14Q + 9Q(squared)+3Q(cubed), what is the marginal cost of producing the fourth unit of output?

A. $42 B. $295 C. $230 D. $116