2010 - fall - midterm - solutions

Optimal choice of l and t will be the combination

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Optimal choice of L and T will be the combination that minimizes the costs of pro- ducing W 1 units. Find the point where the isoquant is tangent to the lowest isocost line. 7
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(c) Suppose that the production of W 1 units of Wheat has a value of $1 . The pro- duction of S 1 units of Solar panels also has a value of $1 : Show the dollar-value isoquant for Solar panels in the °gure below and show the relative prices of the factors of production (the relative input prices) consistent with competitive mar- kets. W 1 L T S 1 Slope is ratio of input prices: w/r 8
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(d) Suppose that there is no substitutability of factors of production and the marginal productivity of a factor of production is constant. Instead of Home±s PPF being as shown in part ( a ) , it will consist of two linear segments. S W The upper, ²atter portion of the PPF corresponds to the economy using all the available land but having some remaining labour, while the lower, steeper portion corresponds to the economy using all the available labour. As before, production of S is labour intensive and the production of W is land intensive. What does the slope of the PPF measure? Explain why the slope is relatively ²at for low S; high W combinations, but it is relatively steep for high S; low W combinations. Slope of the PPF measures the opportunity cost of producing S (good on the hori- zontal axis). ²at portion: relatively ²at PPF suggests the opportunity cost of producing an addi- tional unit of S is relatively low. Over this portion of the PPF the economy is land-constrained and has labour to spare. In order to produce additional unit of S requires relatively large amount of L and small amount of T . The labour is available without giving up any W production. In order to free up some Land, it is necessary to reduce production of W and since T is used intensively in the production of W a small reduction in the production of W will free up a relatively large portion of land ( T ) which can then be used to increase production of S by a large amount. steeper portion: over this portion, the opportunity cost is high. Labour is already constrained. In order to increase production of S , it is necessary to reduce W production. bit since relatively small amounts of L are used in the production of W; it will be necessary to reduce production of W by a relatively large amount in order to free up enough L to produce another unit of S . 9
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