Question

Show that the maximization of output subject to a given cost constraint and minimization of cost

subject to a given output will yield identical results.​

Answer 1

Explanation:

cost constraint than to minimise costs ... answer will be the same (in essence) ... by maximising output subject to a cost y g p j constraint. Let L* be Lagrange, L be labour and K ... For given r, w and y, the firm's cost-.

Answer 2

Maximization of output

Explanation:

• Maximize production at fixed costs: Given the cost of the company and the prices of the two factors of production, the company maximizes profits by increasing output.
• The assumptions used in this study are the same as those used in the previous one. As previously stated, the requirements for the firm's equilibrium are the same. At point P in Figure 17, when the isoquant curve 200 is tangent to the isocost line CL, the company is in equilibrium. Given its cost outlay CL, the company is currently optimising its output level of 200 units by utilising the best combination of OM of capital and ON of labour.
• The company is in equilibrium at the point where the equivalence curve 200 touches the CL line of isokosta.
• It cannot, however, be at points E or F on the isocost line CL, because both The stations in the equivalent 100 produce less output than the equivalent 200.
• By travelling along the isocost line CL from either point E or F to point P, the company can achieve the optimal factor combination level of maximum production.
• Because the firm remains on the same isocost line, this shift incurs no additional costs. Because of the cost constraint, the company cannot achieve a greater level of output, such as isoquant 300.
• As a result, the equilibrium point must be P, with the best factor combination of OM+ ON. The slope of the isoquant curve 200 at point P is the same as the slope of the isocost line CL.
• It means that w/r = L/K = MRTSLK. The isoquant curve must be convex to the origin at the point of tangency with the isocost line as the second criteria.