Question

Suppose a firm, Plant Foods, Inc, uses 3 pounds of Potassium (K) and 10 pounds of Nitrogen (N) to make one pallet of fertilizer (F). PK = $20/lb and PN = $1/lb. Using a graph, sketch the firm’s isoquant and isocost curves for Q = 10 units of output. Also, identify the cost-minimizing combination of K and N. On your graph, put N on the vertical axis and K on the horizontal axis. Make sure your graph is accurate and correctly labeled. You may assume that the amount of K, N, and F are continuous variables.

Answer 1

It shall be noted that 3 pounds of Potassium (K) and 10 pounds of Nitrogen (N) is used to make one pallet of fertilizer (F).

PK = $20/lb and PN = $1/lb.

For Q=10, the pounds of Potassium (K) used = 3*10 = 30 pounds

The pounds of Nitrogen (N) used = 10*10 = 100 pounds

The total cost incurred = 20*30 + 1*100 = $700

Thus, the isoquant representing 30 pounds of Potassium (K) and 100 pounds of Nitrogen (N) to produce Q = 10 and the iso-cost line representing the total cost of $700 is the line that passes through 30 pounds of Potassium (K) and 100 pounds of Nitrogen (N) is: