SHORT RUN COST FUNCTION TC=300+50Q-10Q2+Q3
To find the short-run cost function, we need to observe the equation given: TC = 300 + 50Q - 10Q^2 + Q^3.
In this equation, TC represents total cost, and Q represents the quantity produced. The equation includes three terms: 300, 50Q, and -10Q^2 + Q^3.
The term 300 represents the fixed cost, which is the cost that remains constant regardless of the level of production. In other words, even if no units are produced (Q = 0), there is still a cost of 300.
The term 50Q represents the variable cost, which increases linearly with the level of production. For every unit produced, the cost increases by 50.
The term -10Q^2 represents the cost that changes quadratically with the level of production. As the level of production increases, the cost decreases at an accelerating rate.
The term Q^3 represents the cost that changes cubically with the level of production. As the level of production increases, the cost increases at a decreasing rate.
To find the short-run cost function, simply combine these terms in the equation: TC = 300 + 50Q - 10Q^2 + Q^3.
It is important to note that this equation represents the total cost for a given level of quantity produced (Q). To find the average cost or marginal cost, we would need to divide the total cost by the quantity produced.