From the following equations, determine the price and quantity where the company's supply begins in the short term.
What are the equations provided to determine the price and quantity where the company's supply begins in the short term? How can the variable cost and average variable cost be calculated from these equations?
Equations for Determining Price and Quantity at Company's Supply Start
Equation b: CT = Q³-4Q² + 10Q; CV Q³-4Q+10Q; CVMe=CV/Q
To determine the price and quantity where the company's supply begins in the short term, we first need to calculate the variable cost (CV) from the given equations:
For equation a: CV = Q³-8Q²+12Q
For equation b: CV = Q³-4Q²+10Q
Next, we can find the average variable cost (CVMe) by dividing the variable cost by quantity (Q):
For equation a: CVMe = Q² - 8Q + 12
For equation b: CVMe = Q² - 4Q + 10
The price and quantity where the company's supply begins is at the point where the marginal cost (MC) equals the average variable cost (CVMe). This is calculated as:
For equation a: 3Q²-4Q+90=0; Q = 3 units, MC = $27
For equation b: 3Q²+2Q=0; Q = 0.67 units, MC = $4.45