Suppose a chemical company is in a perfectly competitive industry and has a short run total cost curve of $\mathrm { TC } = \frac { 1 } { 3 } \mathrm { q } ^ { 3 } + 5 \mathrm { q } ^ { 2 } + 10 q + 10$ and a short run marginal cost of SMC = q² + 10q + 10.At the price of 49,how much will be produced?

Question

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In a perfectly competitive market, firms produce where price equals marginal cost (P = MC). Given the price of 49, we set the marginal cost equal to this price to find the quantity produced. The provided marginal cost formula seems to be incorrectly formatted, but assuming it's derived from the total cost (TC) function, the correct marginal cost (MC) should be the derivative of TC with respect to q, which is MC = q^2 + 10q + 10. Setting this equal to 49 and solving for q gives us the quantity produced. The correct calculation should be: 49 = q^2 + 10q + 10, which simplifies to q^2 + 10q - 39 = 0. Solving this quadratic equation, we find that q = 3 is a positive solution that makes sense in this context (the other solution being negative is not feasible for quantity). Therefore, at a price of 49, 3 units will be produced.

Suppose a Chemical Company Is in a Perfectly Competitive Industry TC=13q3+5q2+10q+10\mathrm { TC } = \frac { 1 } { 3 } \mathrm { q } ^ { 3 } + 5 \mathrm { q } ^ { 2 } + 10 q + 10TC=31​q3+5q2+10q+10

Suppose a Chemical Company Is in a Perfectly Competitive Industry $\mathrm { TC } = \frac { 1 } { 3 } \mathrm { q } ^ { 3 } + 5 \mathrm { q } ^ { 2 } + 10 q + 10$