Question

In the space below, draw a firm’s isocost/isoquant diagram with K on the vertical axis and L on the horizontal axis.

1. Show the change that would occur if capital became more expensive and the firm maintained the same total cost.  Be sure to show how each curve changes.  To the right of the graph, clearly indicatewhat happens to the level of output and use of both L and K, and whether you are showing L and K as substitute inputs or complementary inputs.

2. Draw another isocost/isoquant diagram below.  Consider the same increase in the cost of capital.  However, this time, assume the firm maintains the same level of output, so it stays on the same isoquant as the price of capital increases. Show what would change in the graph and to the right of the graph, clearly indicatewhat happens to the firm’s total cost and its use of both L and K.

Answer 1

The production function used would be simple CD production with alpha=0.5, ie we have , and the cost of production would be . For the scenarios, r is doubled here.

(a) The graph is as below.

The initial equilibrium is at point A, for output Q and the budget line being BL. The final equilibrium is at point B, for output Q' and the budget line being BL'. As can be seen, the output decreases since Q'<Q (the isoquant Q' is lower than isoquant Q). Also, the level of employment of K decreases from point A to point B. Hence, as a result of increase in price of K, the level of K used is decreased. The level of L used remains the same as before.

(b) The graph is as below.

The initial equilibrium is at point A, for output Q and the budget line being BL. The final equilibrium is at point B, for output Q and the budget line being BL'. As can be seen, the cost increases since the isocost BL' crosses the isocost BL (if the cost remained the same, the BL' and BL would have the same horizontal intercept, but as can be seen, the horizontal intercept is increased meaning that the cost increased). Also, the level of employment of K decreases from point A to point B. Hence, as a result of increase in price of K, the level of K used is decreased. The level of L used however, increases as a result of increase in price of K. This can be interpreted as that L is relatively cheaper, ie the relative price of L with respect to price of K has decreased since absolute price of L (w) is same and absolute price of K (r) increases.