Question: A firm hires two inputs, input 1 and input 2, to make output. Unfortunately, for every unit of input 1 that the firm hires, 1a1a

A firm hires two inputs, input 1 and input 2, to make output. Unfortunately, for every unit of input 1 that the firm hires, 1a1a units turn out to be defective, where 1>1a>01>1a>0. That is, only a fraction aa of purchased units of input 1 actually contributes to producing output yy. Letx1x1 and x2x2 be the quantities that are not defective and can be employed towards production.

If rounding is needed, please round your answers to 3dp.

A) Suppose the firm's production function is such that x1x1 and x2x2 are perfect substitutes: each unit of output can be made with either one unit of x1x1 or 1414 units of x2x2. Suppose w1=1w1=1 and w2=6w2=6. It is optimal for the firm to hire only input 1 (and hire 0 units of input 2) if aa_______.

B) Suppose the firm's production function is such that x1x1 and x2x2 are perfect complements: the firm needs 1 unit of x1x1 and 55 units of x2x2 to make each unit of output. Find the total cost of producing 7 units of output when w1=w2=1w1=w2=1 and a=0.3a=0.3.

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