Question

PumpkinPlus is a profit-maximizing firm that produces a carving tool using labor and materials according to a production function for which both labor and materials are normal inputs. PumpkinPlus faces a downward-sloping demand curve for carving tools. Say the wage rate rises. What changes do you predict in the use of labor, the use of materials, the number of tools produced, the price per carving tool, and the profit earned by the firm in the long run? Explain your reasoning and mention why you may not be able to predict the direction of certain changes. Provide a sketch of an isoquant/isocost line diagram and a diagram showing demand, marginal revenue, average total cost, and marginal cost to illustrate the old and new amounts of each variable listed.

Answer 1

An increase in wage rate will cause a leftward shift of the supply curve for carving tools, i.e, a contraction of supply. This is because at a given output price, the price of input (labour) has increased, making production of each unit more costly and less profitable. The figure below shows the shift of supply curve from SS to S'S'. Quantity produced falls from Q to Q' and price rises from P to P'.

Number of tools produced: Due to a leftward shift of supply curve, the output of tools will fall, from Q to Q' as shown in the diagram.

Price per carving tool: Price of carving tool will rise, from P to P' as shown in the diagram

The production function of carved tools can be expressed as: Q = f(Labour, Materials)

Use of labour: An increase in the price of labour (i.e., wages) will cause a fall in the amount of labour used in production.This can be concluded from the fact that labour is a normal input, i.e., its demand is inversely proportional to its price.

Use of materials: Materials are the second input in the production of carved tools. Since price of labour has increased, materials are now relatively cheaper. Thus, the producer will replace some labour input with more materials (positive substitution effect). However, the overall output of carved tools has fallen, which means that lesser amounts of both the inputs is required (negative output effect). There is upward pressure on material use due to substitution efffect, and at the same time there is downward pressure due to the output effect.

The figures above depict optimal allocations of labour and materials. In the above figures, IQ₁ is the original isoquant curve, and the isoquant is depicted by the solid downward sloping line. Isoquant 1 is tangent to the isocost curve at point A, with optimal labour and material input at L and M respectively. A rise in wages causes isocost line to pivot inwards, and the new isocost line is depicted by the dotted downward sloping line. The new isoquant curve commensurate with lower output is denoted IQ₂.IQ₂ is tangent to the new isocost at point B, with new optimal labour and material at L' and M' respectively.

Figure 1 depicts the case where positive substitution effect is outweighed by the negative output effect, which causes optimal material input to fall. Figure 2 depicts the case where positive substitution effect dominates over the negative output effect, and the optimal material input rises from M to M'.

The diagram below depicts demand, MR, ATC, and profits before and after the rise in wages.

MC₁ and ATC₁ are the marginal cost and average total cost curves before rise in wages. MC₁ cuts the MR curve from below at point A. Thus, the equilibrium quantity produced is OQ and price is OP. The profit is given by the region RABP.

Te rise in wages causes MC and ATC curves to shift upwards, to MC₂ and ATC₂ respectively. MC₂ cuts MR curve at point A'. Thus the new equilibrium quantity produced is OQ', at price OP'. Profit at the new increased wages is given by the area R'A'B'P'.

So as a result of wage increase, output falls, price rises, and profit falls.