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The figure below shows a production Edgeworth Box, with origins indicated for the inputs of capital, K, and labor, L, into production of goods X and Y. Eight isoquants are shown, reflecting standard constant-returns-to-scale production functions. These are labeled Q0,...,Q7 at the left ends of the isoquants, but it is left to you to know which good, X or Y, these refer to and which of these quantities are larger or smaller than others. For simplicity, we will assume this is a closed economy.
All parts are worth 6 points.
a) Which good is labor intensive?
b) Claim: When operating on the efficiency locus, the economy is "better off" when output of Y is at level Q4 than Q1. In a few sentences, evaluate whether this is true, false, or if you are unable to tell.
c) Draw the PPF for this economy, clearly indicating the outputs of X and Y at various points on the PPF.
d) Suppose the amount of capital available in the economy increases, holding the level of labor constant. Furthermore, suppose the economy, both before and after the change, produces X at the level Q5. How has the w/r ratio (that is, the ratio of labor wage to the rental rate) changed due to the increase in K? [Hint: this is best shown graphically using an Edgeworth box like above.]
e) On the same graph as your PPF for part c, sketch in what the PPF might look like after the increase in capital. You do not need to identify precise points, but the shape of the new PPF should reflect certain facts about the production of this economy.
f) In terms of the national utility level, is the economy better off, worse off or is it impossible to tell, after the capital increase of part d? Briefly explain your answer.