Suppose two neighbours (1 & 2) are deciding upon how many hours 1 and 2 to spend for keeping their common lawn tidy. Average benefits are 1=101+2 and 2=102+1 per hour, implying that neighbours hours increase but own hours decrease benefit as they decrease leisure time. Opportunity costs of lawn hours are constant 1=2=$5.

a) Calculate the Nash equilibrium (NE) hours for both neighbours and draw their best-response functions on a graph indicating the NE. (4+3)

b) Now suppose neighbour 1 could be either low-cost (₁=$3 ) or high-cost (₁=$7 ) type with equal probability and this private information is hidden from neighbour 2, whose cost remains at 2=$5. Calculate the incomplete information or Bayesian-Nash equilibrium (BNE) and the full-information NE (FINE) number of hours. (4+4 )

c) Draw the best-response functions on a graph and clearly indicate the values of the BNE and FINE solutions. A big and clear diagram please. (4)

d) For the high-cost type (1 ), calculate the net benefits or profits (1) for both BNE and FINE hours to determine if neighbour 1 has incentive to disclose his type to neighbour 2. (3)

e) For the low-cost type (1 ), calculate the net benefits or profits (1 ) for both BNE and FINE hours to determine if neighbour 1 has incentive to keep his type hidden from neighbour 2. (3)