The company produces specialised industrial air extraction units and is concerned that, as the market leader, they should be able to make higher profits than they currently are. The firm’s costs are as follows; overheads ‘d’ are £800,000 labour costs per unit ‘e’ are £100 and raw material costs per unit ‘f’ are £258. They also spend £40,000 ‘V’ per period on advertising and are capable of producing up to 1,000 units in each period.
The total cost function is expressed as;
TC = d + eQ + fQ + V
The demand function is as follows;
P = a – bQ + c√V
where a = 4,000, b = 3 and c = 3
1) Lowering the price by 10%. What is the break-even level of output.
2)Doubling the advertising budget. What is the break even level of output? Construct
To answer the first question, we need to find the break-even level of output when the company lowers the price by 10%. The break-even level of output is the point at which the total revenue equals the total cost, resulting in zero profit.
To find the break-even level of output, we can equate the total revenue (TR) to the total cost (TC). The total revenue is calculated by multiplying the price (P) by the quantity (Q), and the total cost is calculated using the cost function.
Given:
Price (P) = a - bQ + c√V (a = 4,000, b = 3, c = 3)
Total cost (TC) = d + eQ + fQ + V (d = £800,000, e = £100, f = £258, V = £40,000)
1) Lowering the price by 10%:
New Price = 0.9 * P
Setting TR = TC and solving for Q:
(0.9 * P) * Q = d + eQ + fQ + V
We substitute the given values and solve for Q:
(0.9 * (a - bQ + c√V)) * Q = d + eQ + fQ + V
(0.9 * (4,000 - 3Q + 3√40,000)) * Q = 800,000 + 100Q + 258Q + 40,000
Now we can solve this equation to find the break-even level of output.