Production

In class, I claimed that in the presence of increasing returns to scale, the price-taking assumption becomes unrealistic and market power has to be taken into account. Demonstrate this claim with a 2-input, 1-output production technology.

Instructions:

Write down a fully specified 2-input, 1-output production technology exhibiting increasing (but not decreasing) returns to scale.

Choose a set of input prices and calculate the firm's cost function. Using the cost function, prove that your production technology exhibits increasing returns to scale.

Given any output price p > 0, what is the firm's optimal production plan?

Choose a demand curve, and explain why the resulting economy has no partial equilibrium when the firm is a price-taker.

Calculate the firm's optimal quantity and price when the firm takes into account the impact of its production on the market price. Draw a diagram illustrating this outcome, and shade in the area representing the dead-weight loss of monopoly on the diagram.

3 Production In class, I claimed that in the presence of increasing returns to scale, the price-taking as sumption becomes unrealistic and market power has to be taken into account. Demonstrate this claim with a 2-input, 1output production technology. Instructions: 0 Write down a fully specied 2input, 1-output production technology exhibiting in- creasing (but not decreasing) returns to scale. 0 Choose a set of input prices and calculate the rm's cost function. Using the cost function, prove that your production technology exhibits increasing returns to scale. 0 Given any output price p > 0, what is the rm's optimal production plan? 0 Choose a demand curve, and explain why the resulting economy has no partial equi- librium when the rm is a price-taker. 0 Calculate the rm's optimal quantity and price when the rm takes into account the impact of its production on the market price. Draw a diagram illustrating this outcome, and shade in the area representing the dead-weight loss of monopoly on the diagram