Question

You are not asked to do questions numbers 2.1 and 2.2 but you must use the functions in 2.1 and 2.2 for the following questions: Explain the meaning of MRS, Calculate also the slope of the budget line curve and explain the meaning of the slope of the problem in the economy. Show the optimum consumption when the slope budget line is the same as the MRS. Give an Explanation of the Economy

PROBLEMS 2.1 Suppose a person has $8.00 to spend only on apples and bananas. Apples cost S.40 each, and bana- nas cost $.10 each. a. If this person buys only apples, how many can be bought? b. If this person buys only bananas, how many can be bought? c. If the person were to buy 10 apples, how many bananas could be bought with the funds left Over? d. If the person consumes one less apple (that is, nine), how many more bananas could be bought? Is this rate of trade-off the same no matter how many apples are relinquished? e. Write down the algebraic equation for this person's budget constraint, and graph it show- ing the points mentioned in parts a through d (using graph paper might improve the accu- racy of your work). 2.2 Suppose the person faced with the budget con straint described in problem 2.1 has preferences for apples (A) and bananas (B) given by 2.4 sum app targ Utility = VA.B a. If A = 5 and B = 80, what will utility be? b. If A = 10, what value for B will provide the same utility as in part a? c. If A = 20, what value for B will provide the same utility as in parts a and b? d. Graph the indifference curve implied by parts a through c. e. Given the budget constraint from problem 2.1, which of the points identified in parts a through c can be bought by this person? f. Show through some examples that every other way of allocating income provides less utility than does the point identified in part b. Graph this utility-maximizing situation. 2.5 ing

Answer 1

Answer .)

MRS is the ratio of the change in the utility of good-1 to the change in the utility of good-2 for the given price level and income.In other words, it measures the rate of change in good - 1 with respect to good- 2 so as to keep the level of utility constant.

Mathematically,

MRS = MU₁/MU₂

Where MU₁ and MU₂ are the marginal utilities of good 1 and good 2 respectively.

Slope of budget line = Price_good1/ Price_good2

Price of good 1 = Price_Apple = $0.40

Price of good 2 = Price_bananas = $0.10

Slope = (0.4/0.1) = 4

The slope of the budget line shows the rate at which good-1 can be consumed with respect to the good-2 keeping the level of expenditure constant.

The optimal point of consumption occurs where,

MRS = Slope of budget line

or,

  MU_apples/ MU_bananas = P_apples / P_{bananas ......eq(1)}

  MU_apples  = (B^1/2) / 2(A^1/2)

Similarly,

MU_bananas  = (A^1/2) / 2(B^1/2)

MRS = B/A

Using eq(1) gives,

B/A = 4

B = 4A .....eq(2)

Budget equation is given as:

P_A(A) + P_B(B) = M ......eq(3)

Where,

P_A = Price of apple

P_B = Price of banana

A = no. of apples

B = no. of bananas

M = Income

Using eq(3) gives,

0.4(A) + 0.1(B) = 8

  

Substituting "B" from eq(2) gives,

0.4A + 0.1(4A) = 8

0.8A = 8

A = 8/0.8

A = 10

Number of apples bought = 10 units

Number of bananas bought = (4A) = 40 units