# The economy of Ping Pong produces its GNP using capital (K) and labor (L). The production function t

The economy of Ping Pong produces its GNP using capital (K) and labor (L). The production function that relates k=K/L and y=Y/L can be described as follows:For capital per capita k between 0 and 3 output is given by y=0.5*k.For k larger than 3 and smaller and equal to 9 an additional unit of k only produces an additional 0.3 units of y. For k larger than 9 an additional unit of k only produces an additional 0.1 units of y.(Hint: This is a production function with diminishing returns that is given by 3 line segments. Sketch the function to get an idea)a)Write down the production function for segments 1) 0< k=”” 2)=””>< k=”” and=”” 3)=””>< kb)what=”” are=”” the=”” capital=”” output=”” ratios=”” (k/y)=”” at=”” k=”3,” 6=”” and=”” 16?c)=”” now=”” suppose=”” ping=”” pong=”” saves=”” 30%=”” of=”” its=”” income=”” and=”” that=”” depreciation=”” is=”” 10%.assume=”” that=”” the=”” population=”” is=”” growing=”” at=”” rate=”” n=”0.02.” write=”” down=”” the=”” equation=”” forcapital=”” accumulation.=”” and=”” then=”” calculate=”” k(t+1)=”” at=”” k(t)=”3,” at=”” k(t)=”6″ and=”” at=”” k(t)=”16.d)What” is=”” the=”” long-run=”” value=”” of=”” k,=”” k*,=”” in=”” ping=”” pong?e)what=”” is=”” the=”” long-run=”” growth=”” rate=”” of=”” per=”” capita=”” income=”” in=”” ping=”” ping?f)what=”” would=”” it=”” be=”” if=”” there=”” was=”” technological=”” progress=”” at=”” the=”” rate=”” of=”” 5%?=””>

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