# Cobbdouglas And Increasing Returns To Scale Please See Picture Below!

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Safeway is one of many grocery stores that offers self-checkout lines and checkout lines with
cashiers. Consider output (y) as the number of customers served per hour, and humans
(cashiers and baggers) and registers are respectively input 1 (X1) and input 2 (m). The old-
fashioned way, one register (X2=1) with one cashier and one bagger (X1=2) can serve on average
100 scanned items per hour (y=100). The new way, four self-checkout registers (X2=4) with one
supervising cashier (X1=1) can serve on average 100 scans per hour (y=100), since customers are
not as fast. In either case, you need both kinds of inputs (labor and capital) to serve customers.
In addition, the more the registers the shorter the lines, so that the average number of
customers served increases by scaling up. w Types of registerlines X1: Employees y: Customers/hour
OseIf-checkout/S old-fashion
m Oself-checkout/lo old-fashion 4000 Gself-checkout/Bold-fashion 4000
m Sself-checkout/O old-fashion
105elf-checkout/0old-fashion —_ 4000 a) The table above shows the results from a sample of 5 stores with different combinations
of old-fashion registers with cashier and bagger, and new self-checkout registers. In a
graph with employees (X1) on the horizontal axis, and registers (X2) on the vertical axis, plot the input combinations for each store. With a line, connect the stores that belong
to the same isoquant. b) With a larger sample of stores, Safeway estimated the following production function: y =
X12X2. What is the marginal product of adding additional personnel (By/OX1)? What is the
marginal product of adding additional registers (By/om)? c) What is the Technical Rate of Substitution between personnel and registers? d) If you double both inputs, does the number of customers served double, more than
double or less than double? Microeconomics