Question

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Answer 1

Solution:

Notice that with technological change (or technological advancement since the cost has decreased, hence increasing efficiency), the marginal cost curve has shifted downwards. To find the total cost saved, we first find the marginal cost functions: the MC curves are straight lines, and using two points formula, we can find the required functions (denoting 1000s of units by x and costs by y)

Finding equation for MC0: straight line passing through (0, 4) and (2, 5.2)

Slope = (5.2 - 4)/(2 - 0) = 0.6

Equation: y - 4 = 0.6(x - 0)

y = 0.6x + 4

Or MC0 = 0.6Q + 4

Then, initial total cost, TC0 = integration of MC0 with respect to Q

TC0 = 0.6*Q²/2 + 4Q + c

With Q = 2000 units, TC0 = 0.6*(2000)²/2 + 4*2000 + c = $1,208,000+c

Similarly, finding equation of MC1: straight line passing through (0, 1) and (2, 1.2)

Slope = (1.2 - 1)/(2 - 0) = 0.1

Equation: y - 1 = 0.1*(x - 0) that is y = 0.1x + 1

Of MC1 = 0.1Q + 1

So, new total cost, TC1 = integration of MC1 with respect to Q

TC1 = 0.1*Q²/2 + Q + c

With Q = 2000 units, TC1= 0.1*(2000)²/2 + 2000 + c = $202,000+c

So, with fixed cost of $c same in both cases, total cost reduced (or saved) = TC0 - TC1

= 1208000 - 202000 = $1,006,000 (to be answered as $1006000)