Please provide wprk and steps for full points Foster Foods, large supermarket, h

Question

Please provide wprk and steps for full points

Foster Foods, large supermarket, has two types of checkout stands: those staffed with human worker (we will call these H), and those that are self-scanners (which we will call S). Human-operated checkout stands can check out 15 customers per hour, while self scanners check out 12 customers per hour. Write the production function in terms of H and S, where q is the number of customers checked out per hour. How can we describe the inputs, H and S, given this functional form? Suppose human checkout stands cost $30 per hour to operate (considering the human wage, plus operating cost for the equipment). Self scanners cost $20 per hour to operate. Suppose our goal is to check out 400 customers per hour. What is the least expensive way to meet this goal? What is the total cost?

Explanation / Answer

a.       The total number of customers served is q and is given by,

q=15H+12S where H is the number of Human operated checkout stands and S is the number of Self Scanners.

A human operated checkout stand can serve 15 customers an hour while self scanners can serve 12 customers an hour. The total output, i.e. customers served is given by the sum of customers served by either type. Hence the two inputs can be considered to be perfect substitutes of each other.

b.      The total cost is given by, C=Ph*H+Ps*S = 30H+20S.

Also we have q=15H+12S=400.

Cost is minimized when the isoquant is tangential to the isocost line, i.e. the slope of the production function is equal to the slope of the isocost line. However in the production function, the inputs substitutes of each other and hence we cannot directly apply the condition for tangency. Since the two are perfect substitutes of each other the optimal action is to choose the cheaper input.

If the slope of the isocost line is greater than that of the production function, i.e the isocost line is flatter, then self scanners are the cheaper input.

And if the isocost line is steeper than the production function, i.e. the slope of the isocost line is greater than the isoquant then human operated checkout stands are cheaper.

Here the slope of the isoquant is = 15/12 =5/4=1.25.

Slope of the isocost line = 30/20 =3/2 =1.5.

Hence the isocost line is flatter.

Therefore to minimize costs, the firm should use only self scanners.

Qx=15H+12S=400 = (15*0)+(12*S)=400,

i.e. S=400/12 = 100/3 =33.33.

They should use 34 self scanners (approx) which comes to a total cost of C=20S = 20*34 = $780.

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.