Suppose Shiva has preferences, as indicated by the following: If he consumes mor

Question

Suppose Shiva has preferences, as indicated by the following: If he consumes more milk (M) than bread (B), then he will always be willing to give up 2 units of milk for 1 additional unit of bread to remain indifferent. If he consumes more bread than milk, however, every time he gives up 1 unit of milk he requires 2 additional units of bread to remain indifferent.

A. With the quantity of milk (QM) on the vertical axis and the quantity of bread (QB) on the horizontal axis, sketch a representative indifference curve for Shiva.

B. What is Shiva’s marginal rate of substitution at any bundle where QM > QB? What is Shiva’s marginal rate of substitution at any bundle where QM < QB?

C. Suppose the price of bread equals 1, the price of milk equals 1, and Shiva’s income is 100. How much milk and bread will Shiva consume in order to maximize his utility? Provide a graph to illustrate your answer.

D. Suppose the price of bread increases to 4, while the price of milk and Shiva’s income remain at the values in part B. How will this affect (i) Shiva’s optimal choice of milk and bread and (ii) his utility (i.e., will his utility increase, decrease, or remain the same)? Provide a graph to illustrate your answer.

Explanation / Answer

A. Let M denote quantity of Milk and B denoote the quantity of bread. When M > B, then MRS = 2/1 = 2, When B > M, then MRS = 1/2. A representative indifference curve is shown in the following figure. On the portion of indifference curve that lies above the line M = B, M is greater than B and thus MRS Is 2. On the portion of indifference curve that lies below the line M = B, B is greater than M and thus MRS is 1/2.

B. MRS may be defined as the number of units of milk the consumer is read to sacrifice to obtain one more unit of bread. The required calculation is done in Part A above.

C. Price ratio = price of bread/ price of milk = 1

For all those bundles on the budget line where M is greater than or equal to B,

     MRS > price ratio

This means for all those bundles on the budget line where M is greater than or equal to B, the number of units milk the consumer is ready to sacrifice to obtain one more unit of bread is greater than the number of units of milk the consumer will be required to sacrifice if he purchases one more unit of bread. This means for all those bundles on the budget line where M is greater than or equal to B, the more the milk is substituted by bread, the better. This further means that of all those bundles on the budget line where M is greater than or equal to B, the consumer prefers the one where M = B.

For all those bundles on the budget line where B is greater than or equal to M,

     MRS < price ratio

This means for all those bundles on the budget line where B is greater than or equal to M, the number of units milk the consumer is ready to sacrifice to obtain one more unit of bread is less than the number of units of milk the consumer will be required to sacrifice if he purchases one more unit of bread. This means for all those bundles on the budget line where B is greater than or equal to M, the more the bread is substituted by milk, the better. This further means that of all those bundles on the budget line where B is greater than or equal to M, the consumer prefers the one where M = B.

This means of all the bundles on the budget line, consumer prefers the bundle where B = M.

The budget line is

(1)Q + (1)M = 100
Q+M = 100
M+M=100
M=50
Q=M=50

Therefore at the optimal bundle Q = M = 50.

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