Final answer:
The firm's marginal cost is MC=15-6Q+3Q². To find the shutdown price, set MC=AVC and solve for Q to find the quantity. Then, substitute the quantity into the total cost function to find the total cost, and divide it by the quantity to get the shutdown price.
Step-by-step explanation:
In order to find the firm's marginal cost, we need to take the derivative of the total cost function with respect to quantity (Q). The derivative of TC=900+15Q-3Q²+Q³ with respect to Q is MC=15-6Q+3Q². Therefore, the firm's marginal cost is MC=15-6Q+3Q².
To find the firm's shutdown price, we need to find the price at which the firm should continue producing in the short run. The shutdown point is where the firm's marginal cost (MC) equals its average variable cost (AVC). So, we set MC=AVC and solve for Q to find the quantity. Then, we substitute the quantity value into the total cost function to find the corresponding total cost. Finally, we divide the total cost by the quantity to find the shutdown price.