# Supply and Demand and Demand Curve

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1. Assume there is a well-deﬁned geographic area of a city. The area is composed exclusively of apartments and is populated by low-income residents. The people who live in the area tend to stay in that area because (1) they cannot aﬀord to live in other areas of the city, (2) they prefer to live with people of their own ethnic group, or (3) there is discrimination against them in other areas of the city. Rents paid are a very high percent of peoples’ incomes. (a) Would the demand for apartments in this area be relatively inelastic or relatively elastic? State why. (b) Would the supply of apartments in this area be relatively inelastic or relatively elastic? State why. 1 (c) Draw the demand and supply curves as you have described them,…show more content…
(b) Suppose the ﬁrm wishes to produce 72 units of output. How much capital and how much labour does the ﬁrm employ? What is the long-run total cost of producing 72 units of output? (c) The ﬁrm suddenly decides to double the quantity of output but only has a day to complete the order. Therefore, in that time, the amount of capital is ﬁxed at the level you found in part (b). The ﬁrm is free to adjust labour hours. How much will it cost to produce 144 units of output? 3 (d) How much would it cost to produce 144 units of output if the ﬁrm could also vary capital? Is this cost higher or lower than the cost you found in part (c)? Explain. 5. Consider a competitive ﬁrm whose short-run cost function is C(q) = 5 + 5q + 5q 2 However, all costs are non-sunk. The ﬁrm faces a market price of p for its output. (a) Derive the ﬁrms proﬁt maximizing condition. Is the suﬃcient second-order condition satisﬁed? (b) What is the lowest price at which the ﬁrm will operate in the short run? (c) Suppose that p = 25. A speciﬁc tax of t(t < p) per unit of output is levied only on this ﬁrm in the industry. What is the proﬁt maximizing level of output q(t) as a function of t? Assume the price is high enough that the ﬁrm does not shut down. (d) What is the tax rate t that maximizes the government revenue T = t.q(t)? 6. In the market for a good there are two types of consumers, ‘heavy users’ and ‘light users’. Each heavy user has