17. For a certain good the production function is given by the equation q = q²qc, where q is the produced output in units of 1000 and qL and qc are the number of units of labour and of capital invested in the production process. Assume that one unit of labour costs 10 units of money and one unit of capital costs 5 units of money. (a) Show on a graph which combinations (qL, qc) generate exactly 64 000 units of output. Put qL on the horizontal axis of the graph and qc on the vertical axis. (b) Explain how one can see on the graph of part a which combinations (qL, qc) allow to produce 64 000 units using a budget of exactly 100 units of money. (c) Explain how one can see on the graph of part a which combinations (qL, qc) allow to produce 64 000 units in the cheapest possible way.
17. For a certain good the production function is given by the equation q = q²qc, where q is the produced output in units of 1000 and qL and qc are the number of units of labour and of capital invested in the production process. Assume that one unit of labour costs 10 units of money and one unit of capital costs 5 units of money. (a) Show on a graph which combinations (qL, qc) generate exactly 64 000 units of output. Put qL on the horizontal axis of the graph and qc on the vertical axis. (b) Explain how one can see on the graph of part a which combinations (qL, qc) allow to produce 64 000 units using a budget of exactly 100 units of money. (c) Explain how one can see on the graph of part a which combinations (qL, qc) allow to produce 64 000 units in the cheapest possible way.
Chapter9: Production Functions
Section: Chapter Questions
Problem 9.4P
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Transcribed Image Text:17. For a certain good the production function is given by the equation q = q²qc, where q is the
produced output in units of 1000 and qL and qc are the number of units of labour and of capital
invested in the production process. Assume that one unit of labour costs 10 units of money and one
unit of capital costs 5 units of money.
(a) Show on a graph which combinations (qL, qc) generate exactly 64 000 units of output. Put qL
on the horizontal axis of the graph and qc on the vertical axis.
(b) Explain how one can see on the graph of part a which combinations (qL, qc) allow to produce
64 000 units using a budget of exactly 100 units of money.
(c) Explain how one can see on the graph of part a which combinations (qL, qc) allow to produce
64 000 units in the cheapest possible way.
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