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ECON 3030 Homework 5 (equilibrium)(100 points total; to get full credit, all work arriving at the answer must be shown)1. (30 points) Suppose the following model of a small local market for burritos works perfectlyin 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 absolutevalue of the slope of the demand curve is greater than the absolute value of the slope of thesupply curve.Concerned about rising costs of public health, local legislature introduces a tax: burritovendors must pay $2 per burrito sold. A local pro-burrito activist, however, claims that asa 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. (30 points) Suppose after carefully studying another market, we concluded that the quantityg of grapefruits demanded at price p is given by g = 30 ? 3p and the quantity suppliedby g = 6p. State government has been imposing a quantity tax at rate t, which it collectsfrom buyers, and this rate t changes from year to year without any obvious logic behind theparticular rate chosen in a particular year.A local grapefruit enthusiast is concerned that in some year the government may choose a taxrate that will actually completely shut down the grapefruit market. Is this possible accordingto the theory we have developed so far? That is, what is the smallest tax rate that will resultin no grapefruits being bought or sold?3. (40 points) In a crowded city far away, the authorities decided that rents were too high. Thesupply function of rental apartments was q = 15 + 3p and the demand function was givenby q = 237 ? 3p, where p is the rent (in $100s to make it realistic). The authorities made itillegal to rent an apartment at more than p = 30. To avoid a housing shortage, the authoritiesagreed to pay landlords enough of a subsidy to make supply equal to demand. How muchwould the subsidy per apartment have to be to eliminate excess demand at the ceiling price?