You are hired as the superintendent in a local student district, and you have to decide how to allocate money between textbooks and computers.
A. What is the optimal allocation rule you should follow when deciding how many textbooks and computers to provide?
B. Suppose the price of computers decreases. How does the optimal allocation of computers change? Assume that both textbooks and computers have diminishing marginal returns. Use the optimal allocation rule as a guide.
Answer A: The allocation of the given money available with the superintendent which has to be allocated between textbooks and computers will be determined by the marginal rate of substitution which is the slope of the indifference curve and the price ratio of textbooks and computers which is actually the slope of the budget line. The Marginal rate of substitution is equal to the ratio of marginal utilities of textbooks and computers respectively.
The MRS and the price ratio have to be equated in order to get the optimal bundle of the quantity of textbooks and computers. The optimal bundle will be at the point where the budget line becomes tangent to the indifference curve which signifies that the utility has been maximized given the constraint of the budget. The marginal rate of substitution tells us the quantity of one good that a person is 'willing' to substitute for a unit quantity of other good whereas the price ratio tells us the rate at which the market allows for the exchange of one good for the other. The equality of these two will give us the optimal bundle since it would mean that the rate at which the consumer is willing to substitute one good for the other is offered and allowed by the market prices too.
Answer B : If the price of the computers falls, the optimal bundle will change because the budget line itself will change and therefore the slope of the budget line will also change. Since the slope of the budget line is equal to the price ratio of textbooks to computers, a fall in price of computers will mean an increase in the slope of the budget line. The new optimal bundle will then be given by the indifference curve at which this new budget line becomes tangential. The new optimal bundle will have more quantity of computers and the person will be on higher indifference curve than before which means greater satisfaction.