1. Suppose the following model of a small local market for burritos works perfectly in predicting the equilibrium: a demand curve, which is a downward-sloping straight line, crosses at one point a supply curve, which is an upward-sloping straight line; the absolute value of the slope of the demand curve is greater than the absolute value of the slope of the supply curve.
Concerned about rising costs of public health, local legislature introduces a tax: burrito vendors must pay $2 per burrito sold. A local pro-burrito activist, however, claims that as a result the equilibrium price paid by consumers will rise by at least $1 and possibly more.
Show whether this claim is consistent with the model.
2. Suppose after carefully studying another market, we concluded that the quantity g of grapefruits demanded at price p is given by g = 30 - 3p and the quantity supplied by g = 6p. State government has been imposing a quantity tax at rate t, which it collects from buyers, and this rate t changes from year to year without any obvious logic behind the particular rate chosen in a particular year.
A local grapefruit enthusiast is concerned that in some year the government may choose a tax rate that will actually completely shut down the grapefruit market. Is this possible according to the theory we have developed so far? That is, what is the smallest tax rate that will result in no grapefruits being bought or sold?
3. In a crowded city far away, the authorities decided that rents were too high. The supply function of rental apartments was q = 15 + 3p and the demand function was given by q = 237 - 3p, where p is the rent (in $100s to make it realistic). The authorities made it illegal to rent an apartment at more than p = 30. To avoid a housing shortage, the authorities agreed to pay landlords enough of a subsidy to make supply equal to demand. How much would the subsidy per apartment have to be to eliminate excess demand at the ceiling price?