Question

Theresa consumes both bagels and toy cars.

A table is shown with four columns. The first column is labeled quantity of bagels, the second column is labeled marginal utility from bagels in utils, the third column is labeled quantity of toy cars, and the fourth column is labeled marginal utility from toy cars in utils. The values in the first column are 1, 2, 3, 4, 5, 6. The values in the second column are 8, 7, 6, 5, 4, 3. The values in the third column are 1, 2, 3, 4, 5, 6. The values in the fourth column are 10, 8, 6, 4, 3, 2.

The table above shows Theresa's marginal utility from bagels and toy cars.

What is her total utility from purchasing three toy cars?

Theresa's weekly income is $11, price of a bagel is $2, and the price of a toy car is $1. What quantity of bagels and toy cars will maximize Theresa's utility if she spends her entire weekly income on bagels and toy cars? Explain your answer using marginal analysis.

Assume that the price of wheat, an input for the production of bagels, increases. Will Theresa's demand for bagels increase, decrease, or not change? Explain.

Suppose that Theresa's income elasticity for bagels is -0.2.Does the value of Theresa's income elasticity indicate that bagels are normal goods, inferior goods, substitutes, or complements?

Suppose that when the price of toy cars increases by 10 percent, Theresa buys 5 percent fewer toy cars and 4 percent less of a different toy, blocks. Calculate the cross-price elasticity for toy cars and blocks and indicate if it is positive or negative.

Keep every answer within a sentence and if its a graph describe how to draw it and show work

Answer 1

Total utility from 3 toy cars = 10 + 8 + 6 = 24 utils.

Compute MU per dollar: bagels MU/$ = {8/2=4, 7/2=3.5, 6/2=3, 5/2=2.5, 4/2=2, 3/2=1.5} and toy cars MU/$ = {10/1=10, 8, 6, 4, 3, 2}; spending $11, buy goods in descending MU/$ order (ties broken arbitrarily) until money exhausts, which yields 5 toy cars ($5) and 3 bagels ($6) for a utility-maximizing bundle of 3 bagels and 5 toy cars (the last marginal MU/$s equalize at 3).

If the price of wheat rises, bagel production costs (and likely the price of bagels) rise, reducing Theresa’s demand for bagels because their MU per dollar falls.

An income elasticity of -0.2 (negative) indicates bagels are an inferior good.

Cross-price elasticity of blocks with respect to the price of toy cars = (%Δquantity of blocks)/( %Δprice of toy cars) = (-4%)/(+10%) = -0.4, which is negative, so blocks and toy cars are complements.