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March 29, 2017

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1) Lowering the price by 10%. What is the break-even level of output?

The company produces specialized glass 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 ‘X’ 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 + X
The demand function is as follows;
P = a – bQ + c√X
where a = 4,000, b = 3 and c = 3.

2) Doubling the advertising budget. What is the break- even level of the output?

  • Maths - ,

    The company produces specialized glass 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 ‘X’ 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 + X
    The demand function is as follows;
    P = a – bQ + c√X
    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 the output?

  • Economics - ,

    Interestingly, you are asking for the break-even level of output rather than the profit-maximizing level. Hummm.

    Anyway. This is simply an algebra problem. First collapse the two Q terms in TC. So, TC=800,000+358Q + 40000
    Total Revenue is P*Q. So, TR=4000Q-3Q^2 + 600Q
    Set TC=TR and solve for Q (subject to the constraint that Q<=1000)

    1) Repeat cept multiply all terms in the TR equation by 0.90
    2) Repeat cept change advertising by 40K.

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